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![Page 1: Time domain harmonic state estimation using filtered measurements based on fourier transform for unbalanced power system conditions](https://reader036.fdocuments.in/reader036/viewer/2022070513/5882f2a21a28ab3f1e8b5ed5/html5/thumbnails/1.jpg)
Time-Domain Harmonic State Estimation Using Filtered
Measurements based on Fourier Transform for Unbalanced Power
System Conditions Ismael Molina-MorenoAurelio Medina-Ríos
Rafael Cisneros-Magaña
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AgendaO IntroductionO ProposalsO ResultsO Conclusions
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IntroductionO Harmonic state estimation (HSE) has
conventionally been formulated in the frequency-domain, i.e. using power quality meters. However, it is possible doing similar analysis in the time-domain, i.e. using voltage and current waveform meters.
O Power quality meter has two main parts: data acquisition systems (DAQ) and a processing units to determine the harmonics components. So, if only the DAQ is used then the meters become more economical.
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IntroductionO The estimation implies a limited
number of monitoring devices, so the placement of them is another challenge task. Prior works have not considered this limitation.
O The initial state is also required by prior methodologies due to formulation is based on numerical integration methods.
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IntroductionO A particular prior technique in the
time-domain for HSE has been based on Kalman Filter.
O This methodology requires the harmonic sources, the error matrices associated with the measuring process and the plant model.
O The optimal meter placement and the initial state are also required.
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Proposed methodologyO The proposed methodology to estimate
the harmonic state is shown in Fig. 1.
O Time-domain harmonic state estimation (TDHSE) is in the discrete time and is based on filtered measurements.
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Proposed methodologyO The proposed methodology to estimate
the harmonic state is shown in Fig. 1.
O Time-domain harmonic state estimation (TDHSE) is in the discrete time and is based on filtered measurements.
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Proposed methodologyO The mathematical formulation for
the proposed methodology is given in (1) and (2)
O k is de kth sample. N samples are taken to complete a cycle.
O The first step is to filter z to mitigate the error e.
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Proposed methodologyO The filter is based on Fourier transform:O Function represented by Fourier coefficients
O In the discrete time-domain
O The key consist in consider only the harmonic coefficients of interest when the measurement be rebuilt
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Proposed methodologyO The second step is develop a mathematical formulation
to relate the measurements with state variable in the discrete-time.
O To discretize the continuous time differential equations, the central method is used
O Preliminary results have been reported in the North American Power Symposium 2015.
O The proposed method has been extended to unbalanced case where it is necessary model the network by a three-phase circuit.
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ResultsO 12 measurements
instead of 27 to obtain similar results.
O Unbalanced condition.
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ConclusionsO A methodology for time domain harmonic state estimation for
unbalanced case assessment in power networks using filtered measurements based on Fourier transform has been proposed.
O The performance of the proposed methodology has been validated through direct comparison of the estimated state variables against the actual variables response. In all the analyzed cases a close agreement between the estimated and the actual response has been achieved.
O The proposed methodology does not require an accurate previous knowledge of the harmonic sources nor initial conditions. It only needs of a snapshot of voltage and current during at time interval of interest to estimate the harmonic state.
O Although the accuracy of estimation depends on device placement, the error due to location has been relatively small, i.e. for the analyzed cases it has been kept below 0.23%.